A numerically efficient finite-element formulation for the general waveguide problem without spurious modes

Svedin, Jan

doi:10.1109/22.41035

Cited by 58 publications

(13 citation statements)

References 15 publications

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“…Funhennore, in the full vectorial fonnulation [1]- [10] the propagat ion conslant is fi rsl given as an inpul datum , and subsequently the operating frequency is obtained as a solution. More recently, several methods for solving directly the propagation constant have been developed , but each has its drawback, e.g., a large number of field components (11] - [13) , consideration of the adjoint fi eld which does not correspond to the actual electromagnet ic field [14], o r the need to estimate the line integral in the varialional expression [1 5). IEEE' Log Nu mber9104779.…”

Section: Introductionmentioning

confidence: 99%

Simple and efficient finite-element analysis of microwave and optical waveguides

Koshiba

Inoue

1992

IEEE Trans. Microwave Theory Techn.

103

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Abstract-A simple and efficient ftnite.element method for the analysis or microwave and optical waveguiding problems is formulated using three components of the electric or magnetic field . In order to eliminate spurious solutions, edge elements are introduced. In the edge element approach the nodal parameters are not limited to the magnetic fi eld as in the conventional three-component formulation ror the dielectric waveguiding problem. An eigenvalue equation derived here involves only the edge variables in the transversal plane and ca n provide a direct solution ror the propagation constant. To show the vailidity and usefulness of this approach, computed results are illustrated fo r microstrlp transmission lines and dielectric waveguides. I. I NTRODUCTIONTO RIGOROUSLY evaluate propagat ion characteris-1. tics of microwave and optical wavegu ides with arbitrarily shaped cross sections, vectorial wave analys is is necessary , and different types o f the vector finit e-element method (FEM) have been developed . Of the various formulations, the FEM using full vector H field is quite suitable for a wide range of practical, complicated problems [I ] -[ I OJ . Thi s approach has been widely used fo r various dielectric waveguiding structures in microwave , millimeter-wave , and optical wavelength regions, and recently has been utilized as the waveguide solver of CAD packages [7] . The most serious problem associated with this approach is the appearance of spurious solutions. The penalty fun ction method [31. [4] , (6) , [7] has been used to cure this problem, but in this technique an arbitrary positi ve constant , ca lled the penalty coeffi cient , is involved and the accuracy of solutions depends on its magnitude . Funhennore, in the full vectorial fonnulation [1]-[10] the propagat ion conslant is fi rsl given as an inpul datum , and subsequently the operating frequency is obtained as a solution. More recently, several methods for solving directly the propagation constant have been developed , but each has its drawback, e.g., a large number of field components (11] -[13) , consideration of the adjoint fi eld which does not correspond to the actual electromagnet ic field [14], o r the need to estimate the line integral in the varialional expression [1 5). IEEE' Log Nu mber9104779.In this paper a simple and efficient FEM fo r the analysis of microwave and optical waveguiding problems is formulated using three components of the electric or magnetic fi eld. [n order to el iminate spurious solut ions and 10 treat arbitrarily shaped waveguidcs, triangu la r edge elements are introduced . An e igenvalue equation derived here invo lves only the edge variables in the transversal plane and can prov ide a direct solution fo r the propagation constant. To show the validity and usefulness of this approach, examples are computed fo r microstrip transmission lines on isolropic or ani sotropic substrates, dielectric rectangular wavegu ides, and equi lateral triangular core waveguides. II . B ASIC EQUATIONSWe consider a dielectric...

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Section: Introductionmentioning

confidence: 99%

Simple and efficient finite-element analysis of microwave and optical waveguides

Koshiba

Inoue

1992

IEEE Trans. Microwave Theory Techn.

103

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“…Schulz (2003) developed an adjoint high-order vectorial finite element method for nonsymmetric transversally anisotropic waveguides. Svedin's (1989Svedin's ( , 1990aSvedin's ( , 1990b six-components formulation is not efficient and bears a considerable cost of computing resources. Nuno et al (1999) proposed an E-formulation to analyze lossy gyrotropic structures but this had the disadvantage of generating nonvalid zero eigenvalues solutions in the transformation process.…”

Section: Gyroelectric Finite Element Formulationmentioning

confidence: 99%

Finite Element Analysis of Millimeter and Sub-Millimeter Wave Gyroelectric Waveguide Components

et al. 2006

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Gallium arsenide (GaAs) and indium antimonide (InSb) are two candidate semiconductor materials for supporting nonreciprocal behavior at millimeter wave and sub-millimeter wave frequencies. Each material is characterized as a function of bias field/frequency and different operating regions are identified either side of the extraordinary wave resonance. An eigenvalue finite element formulation is developed to calculate the complex propagation constant for general gyroelectric waveguide structures. The solver is used to investigate nonreciprocal phase shift and attenuation in a transversely magnetized, semiconductor slab loaded waveguide in the various operating regions. Several potential regions of isolation and differential phase shift have been identified for exploitation in the millimeter wave range for GaAs and in the sub-millimeter wave range for InSb.

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“…Recently, several different ways to avoid spurious solutions in the FEM analysis of waveguide problem has been developed. [18][19][20] The edge element is one of the popular methods that has been employed successfully for vector formulations without resulting in "spurious solutions." The FEM based on the edge elements is widely used to address the microwave engineering problems including lossy and anisotropic waveguides.…”

Section: Propagation Properties Of Smart Nrd Waveguidementioning

confidence: 99%

Smart millimeter-wave devices using liquid crystal

et al. 2004

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Smart liquid crystal (LC) millimeter-wave (MMW) electronic devices are demonstrated using the electricallycontrollable permittivity through LC directors' reorientation. In this paper, we review the LC classes and its important physical properties for the proposed applications. Some commercially available LCs exhibit a relatively large birefringence (∆n~0.2) in MMW bands and, therefore, are useful for millimeter wave devices. A nonradiative dielectric waveguide using LC is proposed and characterized using numerical simulations. The simulation results show that the LC waveguide is promising for future MMW technologies.

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A numerically efficient finite-element formulation for the general waveguide problem without spurious modes

Cited by 58 publications

References 15 publications

Simple and efficient finite-element analysis of microwave and optical waveguides

Simple and efficient finite-element analysis of microwave and optical waveguides

Finite Element Analysis of Millimeter and Sub-Millimeter Wave Gyroelectric Waveguide Components

Smart millimeter-wave devices using liquid crystal

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